Robust trend inference with series variance estimator and testing-optimal smoothing parameter

The paper develops a novel testing procedure for hypotheses on deterministic trends in a multivariate trend stationary model. The trends are estimated by the OLS estimator and the long run variance (LRV) matrix is estimated by a series type estimator with carefully selected basis functions. Regardle...

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Bibliographic Details
Published in:	Journal of econometrics 2011-10, Vol.164 (2), p.345-366
Main Author:	Sun, Yixiao
Format:	Article
Language:	eng
Subjects:	[formula omitted]-distribution Applications Asymptotic expansion Asymptotic expansion F-distribution Hotelling's T2 distribution Long run variance Robust standard error Series method Testing-optimal smoothing parameter choice Trend inference Type I and type II errors Asymptotic methods Distribution Economic models Estimating techniques Estimation Exact sciences and technology Hotelling’s [formula omitted] distribution Insurance, economics, finance Long run variance Mathematics Model testing Multivariate analysis Nonparametric inference Parameter estimation Parametric inference Probability and statistics Probability theory Regression analysis Robust standard error Sciences and techniques of general use Series method Significance tests Statistical models Statistics Studies Test methods Testing-optimal smoothing parameter choice Trend inference Type I and type II errors
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Summary:	The paper develops a novel testing procedure for hypotheses on deterministic trends in a multivariate trend stationary model. The trends are estimated by the OLS estimator and the long run variance (LRV) matrix is estimated by a series type estimator with carefully selected basis functions. Regardless of whether the number of basis functions K is fixed or grows with the sample size, the Wald statistic converges to a standard distribution. It is shown that critical values from the fixed- K asymptotics are second-order correct under the large- K asymptotics. A new practical approach is proposed to select K that addresses the central concern of hypothesis testing: the selected smoothing parameter is testing-optimal in that it minimizes the type II error while controlling for the type I error. Simulations indicate that the new test is as accurate in size as the nonstandard test of Vogelsang and Franses (2005) and as powerful as the corresponding Wald test based on the large- K asymptotics. The new test therefore combines the advantages of the nonstandard test and the standard Wald test while avoiding their main disadvantages (power loss and size distortion, respectively).
ISSN:	0304-4076 1872-6895